Phonon dispersion curves for perfect crystals of the body-centered cubic metals were calculated by using the ab initio force-constant method in a super-cell approach. It was shown that the coupling constants of Li decayed much more slowly in space than did those of Na or K. Therefore, the phonon spectrum for Li could not be reliably determined by using the super-cell sizes which were used in the calculations. From the phonon spectra of a perfect super-cell, and for a super-cell with a monovacancy, the vacancy-formation entropy was deduced to be equal to 1.36k for Na and 0.78k for K. Formation energies of 0.53, 0.34 and 0.30eV (and a formation volume of about half of an atomic volume) were obtained for Li, Na and K, respectively. The temperature and pressure dependences of the formation entropy and volume were investigated for the case of Na, and a marked decrease in the formation volume with increasing pressure was found. The migration energies and volumes were determined within the framework of transition-state theory. The migration energies were small (about 0.05eV) for Li, Na and K, and the migration volumes were small and negative for Li and Na. The calculated activation energies for self-diffusion (0.58, 0.39, 0.35eV) agreed well with experimental data. By neglecting the migration entropy, and inserting the Flynn expression for the attempt frequency, absolute values of the self-diffusion coefficients were determined as a function of temperature. In the case of Na, these values agreed well with experimental data whereas, for K, the calculated values were too small; except at low temperatures.

Theory of Self-Diffusion in Alkali Metals - Results for Monovacancies in Li, Na and K. V.Schott, M.Fähnle, P.A.Madden: Journal of Physics - Condensed Matter, 2000, 12[7], 1171-94